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This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information can depend on both predictors and the response variables. Our proposed approach involves two steps: First we construct a family of models (possibly infinite dimensional) indexed by the unknown parameter of the missing probability mechanism. In the second step, a search is carried out to find the empirically optimal member of an appropriate cover (or subclass) of the underlying family in the sense of minimizing the mean squared prediction error. The main focus of the paper is to look into some of the theoretical properties of these estimators. The issue of identifiability is also addressed. Our methods use a data-splitting approach which is quite easy to implement. We also derive exponential bounds on the performance of the resulting estimators in terms of their deviations from the true regression curve in general L p norms, where we allow the size of the cover or subclass to diverge as the sample size n increases. These bounds immediately yield various strong convergence results for the proposed estimators. As an application of our findings, we consider the problem of statistical classification based on the proposed regression estimators and also look into their rates of convergence under different settings. Although this work is mainly stated for kernel-type estimators, it can also be extended to other popular local-averaging methods such as nearest-neighbor and histogram estimators. [ABSTRACT FROM AUTHOR]

This paper examines the concepts and practical applications of the spanning tree protocol (STP). It also covers per-VLAN spanning tree (PVST), multiple spanning tree (MST), and rapid STP (RSTP). Moreover, practical scenarios are presented to help the reader understand the concepts and implementations of these protocols. This study analyzes protocols using seven metrics. All protocols have been evaluated using these metrics in both small and big topology scenarios to obtain the best results. In addition, all metrics are mentioned in the introduction chapter, and the way used to apply tests on the metrics is described in the methodology chapter. Based on the experiments, different STPs performance are compared, including STP, RSTP, PVST, and MST. In summary, findings show that STP is easy to use and performs well overall, but it consistently has high latency issues. RSTP is suitable for small networks and has quick convergence, but it cannot handle as much load as STP. PVST performed the best in the experiments, as it demonstrated high scalability and the ability to handle a lot of pressure, although it requires strong hardware. However, MST did not perform as well as expected, as it struggled with delay problems and high jitter. In conclusion, it is recommended to use RSTP for simple networks that require fast convergence with dependable delay and capacity, or STP for networks that require good scaling and bandwidth. PVST is an excellent option for those who can afford high-performance hardware, while MST is suitable for simple networks or those with outdated hardware. [ABSTRACT FROM AUTHOR]

This paper analyses the self-representations of Portuguese media professionals and their work practices. Utilizing data from a broader empirical study, this paper delves into the dynamics of influence among various actors within newsrooms. Based on journalists' perceptions of the content, the methods they use to assess the quality of the news are also identified. To address these enquiries, a survey was conducted among professionals engaged in the news production process. This sample comprised 72 individuals from various sectors of newsrooms, including photographers, designers, IT professionals, social media managers, and videographers. The main results indicate that seven out of ten respondents acknowledged their reliance on colleagues in newsrooms for success. Furthermore, the data suggest that there are no significant disparities among different professionals, with personal satisfaction emerging as the primary criterion for assessing the work quality. It is notable that almost twice as many women tend to indicate the low impact of the journalist on their work compared to male respondents. Moreover, most respondents stated that there is space for hybrid professionals in newsrooms. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the numerical solution of the Brusselator system using a meshless method. A numerical scheme is derived employing the formulas of the Generalized Finite Difference Method, and the convergence of the approximate solution to the exact solution is examined. In order to demonstrate the applicability and accuracy of the method, several examples are proposed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the product of resolvents of a finite number of monotone vector fields on a Hadamard manifold to approximate both the singular points of their sum and a common singular point among them. For the sum of any finitely many maximal monotone vector fields, with some suitable assumptions, it is proved that the obtained sequence of the iterative method is convergent. The paper ends with some examples and applications. [ABSTRACT FROM AUTHOR]

In this paper, the development and analysis of a proposed method for solving physical models arising from real-life scenarios are presented. The proposed method is derived via the transcendental function of exponential type, examined and studied for its properties. In addition, the effectiveness of the method is evaluated by applying it to three numerical examples that originated from real-world scenarios. Moreover, this study presents a comparison of the outcomes generated by the proposed method and the existing method, in the context of the exact solution. The study concludes that the proposed method solves real life problems with the expected level of accuracy and, therefore, can be considered among the numerous methods that are appropriate and suitable for solving first-order initial value problems (IVPs). [ABSTRACT FROM AUTHOR]

In this paper, we intend to utilize the generalized scalar auxiliary variable (GSAV) approach proposed in recent paper (Ju et al., SIAM J. Numer. Anal., 60 (2022), 1905–1931) for the nonlocal coupled sine-Gordon equation to construct a class of fully decoupled, linear, and second-order accurate energy-preserving scheme. The unconditional unique solvability and discrete energy conservation law of the proposed scheme are rigorously discussed, and the unconditional convergence is then proved by the mathematical induction. Particularly, the convergence analysis covers the proposed scheme in multiple dimensions due to the corresponding nonlinear terms satisfy the global Lipschitz continuity straightforwardly. Finally, time evolution of dynamical behavior of the governing equation with different nonlocal parameters are observed, and ample numerical comparisons demonstrate that the proposed scheme manifests high efficiency in long-time computations. [ABSTRACT FROM AUTHOR]

Purpose: This study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method. Design/methodology/approach: We present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method. Findings: The paper provides empirical insights into how to solve a system of absolute value equations. Originality/value: This paper fulfills an identified need to study absolute value equations. [ABSTRACT FROM AUTHOR]

In this paper, we study a method of polynomial interpolation that lies in-between Lagrange and Hermite methods. The novelty is that we use very general nodal systems on the unit circle as well as on the bounded interval only characterized by a separation property. The way in which we interpolate consists in considering all the nodes for the prescribed values and only half for the derivatives. Firstly, we develop the theory on the unit circle, obtaining the main properties of the nodal polynomials and studying the convergence of the interpolation polynomials corresponding to continuous functions with some kind of modulus of continuity and with general conditions on the prescribed values for half of the derivatives. We complete this first part of the paper with the study of the convergence for smooth functions obtaining the rate of convergence, which is slightly slower than that when equidistributed nodal points are considered. The second part of the paper is devoted to solving a similar problem on the bounded interval by using nodal systems having good properties of separation, generalizing the Chebyshev–Lobatto system, and well related to the nodal systems on the unit circle studied before. We obtain an expression of the interpolation polynomials as well as results about their convergence in the case of continuous functions with a convenient modulus of continuity and, particularly, for differentiable functions. Finally, we present some numerical experiments related to the application of the method with the nodal systems dealt with. [ABSTRACT FROM AUTHOR]

In this study, we extended the applicability of a derivative-free algorithm to encompass the solution of operators that may be either differentiable or non-differentiable. Conditions weaker than the ones in earlier studies are employed for the convergence analysis. The earlier results considered assumptions up to the existence of the ninth order derivative of the main operator, even though there are no derivatives in the algorithm, and the Taylor series on the finite Euclidian space restricts the applicability of the algorithm. Moreover, the previous results could not be used for non-differentiable equations, although the algorithm could converge. The new local result used only conditions on the divided difference in the algorithm to show the convergence. Moreover, the more challenging semi-local convergence that had not previously been studied was considered using majorizing sequences. The paper included results on the upper bounds of the error estimates and domains where there was only one solution for the equation. The methodology of this paper is applicable to other algorithms using inverses and in the setting of a Banach space. Numerical examples further validate our approach. [ABSTRACT FROM AUTHOR]

Some new classes of general harmonic convex sets and convex functions are introduced and studied in this paper. The optimality criteria of the differentiable general harmonic functions is characterized by the general harmonic variational inequalities. Special cases are also pointed out as applications of the new concepts. Auxiliary principle technique involving an arbitrary operator is applied to suggest and analysis several inertial type methods are suggested. Convergence criteria is investigated of the proposed methods under weaker conditions. The results obtained in this paper may inspire further research along with implementable numerical methods for solving the general harmonic variational inequalities and related optimization problems. [ABSTRACT FROM AUTHOR]

Digital, economic, and societal development has prompted the industry to shift its focus from offering products or services to bundles of products and services. Given the breadth of product- service systems in the modern economy, it is becoming increasingly important to consider how they should be regulated at the EU level. This paper investigates whether the traditional distinction between goods and services in EU free movement law applies to product-service systems. To this end, EU primary law, specifically the distinction between goods and services under Article 26(2) of the TFEU, is examined. The argument of this paper builds on the body of case-law of the CJEU where the predominance test was applied to traditional cases of product-service bundles and the medium test to cases with a digital component. It proposes a functional, normative, and constitutional inquiry to determine whether product-service systems fall under the rules governing free movement of goods, services, or a sui generis category. It concludes that coherence of EU law, rather than convergence of the two freedoms, is required to ensure predictability and legal certainty for business owners and consumers. [ABSTRACT FROM AUTHOR]

The paper presents an iterative scheme called the general tensor regular splitting iterative (GTRS) method for solving the multilinear PageRank problem, which is based on a (weak) regular splitting technique and further accelerates the iterative process by introducing a parameter. The method yields familiar iterative schemes through the use of specific splitting strategies, including fixed-point, inner-outer, Jacobi, Gauss-Seidel and successive overrelaxation methods. The paper analyzes the convergence of these solvers in detail. Numerical results are provided to demonstrate the effectiveness of the proposed method in solving the multilinear PageRank problem. [ABSTRACT FROM AUTHOR]

Systems engineering (SE) solves the most complex problems, bringing together societal issues, theoretical engineering, and the transformation of theory into products and services to better humanity and reduce suffering. In industry, the effort to transform theoretical concepts into practical solutions begins with the product life cycle concept stage, where systems engineering estimates and derives technologies, costs, and schedules. It is crucial to have a successful concept stage as today's industries focus on producing the most capable technologies at an affordable cost and faster time to market than ever before. The research of this paper utilizes a transdisciplinary SE process model in the concept stage to develop and propose training for early-in-career engineers, effectively bridging the gap from university learning to industry practice. With a focus on the concept stage of the product life cycle and the industry's demands of expeditiously proposing complex technical solutions, the paper aims to create an efficient learning program. The main objective of this research is to create a learning program to bring up-to-speed early-in-career engineers using a transdisciplinary SE process model, with six key components: (1) disciplinary convergence—creating a collective impact; (2) TD collaboration; (3) collective intelligence; (4) TD research integration; (5) TD engineering tools; and (6) analysis and TD assessment. The research will then conclude with a case study piloting the TD learning program and analyzing its effectiveness, ultimately aiming to enhance early-in-career engineers' skills in proposing technical solutions that meet customer demands and drive business profitability. [ABSTRACT FROM AUTHOR]

The paper argues that Roque J. Ferriols [1924-2021] and Leonardo N. Mercado [1935-2020] simultaneously converge and diverge in their understanding of the value of the Philippine languages in the flourishing of Filipino philosophy. On the one hand, these philosophers converge in seeing the vitality of local languages in philosophizing. On the other hand, they diverge because Ferriols' trajectory is centrifugal while Mercado's is centripetal. Ferriols' centrifugal orientation is conditioned by his belief that there is no Filipino philosophy and that developing one is a pointless endeavor. Mercado's centripetal orientation is conditioned by his belief that a local language is a locus for philosophical investigation because it mirrors a worldview. In this paper, I first show their point of convergence by exploring the context that disposes them to focus their attention on a local language. Second, I show that their point of divergence is seen in the way they see a local language: Ferriols sees it as a way to express a worldview, while Mercado sees it as a way to investigate a worldview. Third, I propose that a synthesis of the thoughts of these two influential Filipino priest-philosophers contributes to the ongoing study on the development of Filipino philosophy in the postmodern Philippines. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present a finite difference scheme that estimates the solution of space fractional diffusion equation with the Caputo fractional derivative. The proposed scheme's stability, and convergence are proved. To assess the efficiency of this program, a set of tests is carried out. The results of these tests demonstrate the reliability and accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]

Background: Online interaction in blended learning is leveraged through social presence and convergence. However, little systematic work currently exists on how researchers have explored these challenges in higher education institutions and no studies have synthesised these challenges. Objectives: The purpose of this study is to give a novel overview of social presence and convergence to improve online interaction in blended learning in higher education. The findings will be synthesised into blended learning design principles. Method: Two systematic literature reviews, one on each challenge, were carried out through the Web of Science databases and consulting cited sources in review articles. Accordingly, 28 distinct studies were selected through the guidelines of the PRISMA statement, using predefined selection criteria. Results and Conclusions: The results show that social presence in blended learning is mostly evoked through course design, introductory f2f meetings, collaborative activities, prompt online feedback, the teacher's presence, and planned facilitation. To establish convergence, it is recommended to make basic theory available online through video clips, web‐lectures, articles, followed by simple online assignments or self‐study to increase understanding, thereby creating opportunities for deep learning during face‐to‐face through discussions and collaborative activities. Implications: This paper adds to the theory on blended learning and instructional design in higher education, and further offers an elaborate set of design principles for educational practice. Future research on instructional design may investigate in particular how a target group or student factors, are affected by the blended learning environment in order to tailor designs for a specific target group. Lay Description: What is known?: Online interaction is pivotal in blended learningOnline interaction is leveraged through social presence and convergenceSocial presence prevents the online student from feeling lonelyConvergence entails deciding the best‐suited delivery mode: online or face‐to‐face What this paper adds: A novel overview and critical analysis of social presence in blended learningA novel overview and critical analysis of convergence in blended learningA synthesis of the findings on social presence and convergenceExtraction of the findings into blended learning design principles Implications for practitioners: The teacher's presence through design and accessibility fosters students' social presencePlacing concepts online leaves room for deep learning during face‐to‐faceCollaborative activities evoke social presence and facilitate deep learningBlended learning designs should be further tailored for the target group [ABSTRACT FROM AUTHOR]

This paper reports on research into co-creation labs as a tool for exploring environmental communication. Co-creation labs are novel spaces for experimentation, social learning, and trans-disciplinary as well as cross-sectoral collaboration for sustainability transformations. This paper examines the approach taken by researchers to theorising, via a repurposing of the 2×2 scenario matrix, a series of "labs" that represent diverse spaces in which to explore co-creative convergence through transformative learning processes. In addition, examples from work done to date are offered to illustrate progress in implementing these labs and testing the strengths and weaknesses of these co-creative spaces. [ABSTRACT FROM AUTHOR]

In the paper, the sufficient conditions are found for the convergence, summability by the Cesàro methods and unconditional convergence almost everywhere of orthogonal series, which are equivalent to the well-known theorems of Menshov–Redemacher, Menshov, and Orlich. [ABSTRACT FROM AUTHOR]

This paper presents three tensor randomized extended Kaczmarz methods for solving a tensor inconsistent linear system of equations under the t-product between tensors. The randomized extended Kaczmarz, the randomized extended block Kaczmarz, and the randomized extended greedy block Kaczmarz methods in tensor form are proposed to solve inconsistent tensor linear system of equations, respectively. The convergence of each method is proved. Several numerical examples are given to show the efficiency and effectiveness of our methods. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new splitting characteristic finite difference scheme for solving the time-fractional mobile-immobile nonlinear advection–diffusion equation by combining non-overlapping block-divided domain decomposition method, the operator splitting technique and the characteristic finite difference method. Over each sub-domain, the solutions and fluxes along x-direction in the interiors of sub-domains are computed by the implicit characteristic finite difference method while the intermediate fluxes on the interfaces of sub-domains are computed by local multi-point weighted average from the approximate solutions at characteristic tracking points which are solved by the quadratic interpolation. Secondly, the solutions and fluxes along y direction in the interiors of sub-domains are computed lastly by the implicit characteristic difference method while the time fractional derivative is approximated by L1-format and the intermediate fluxes on the interfaces of sub-domains are computed by local multi-point weighted average from the approximate solutions at characteristic tracking points are solved by the quadratic interpolation. Applying Brouwer fixed point theorem, we prove strictly the existence and uniqueness of the proposed scheme. The conditional stability and convergence with O Δ t + Δ t 2 - α + h 2 + H 5 2 of the proposed scheme are given as well. Numerical experiments verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an improved zeroing neural network (ZNN) model is proposed to obtain the positive definite solutions of the continuous coupled Lyapunov matrix equations (CLMEs) associated with continuous‐time Markovian jump (CMJ) systems. To achieve this, a general ZNN model is established by constructing a matrix‐valued error function. Then, to accelerate the convergence rate of the proposed ZNN model, the latest estimation is introduced to obtain an improved ZNN model. Some convergence conditions have been derived for the presented improved ZNN model through Lyapunov theory. Comparisons among the improved ZNN model and the existing results are conducted to illustrate the advantages of the proposed improved ZNN model in numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distributed approximate subgradient-type method for minimizing a sum of differentiable and non-differentiable convex functions subject to nondifferentiable convex functional constraints in a Euclidean space. We establish the convergence of the sequence generated by our method to an optimal solution of the problem under consideration. Moreover, we derive a convergence rate of order O(N1−a) for the objective function values, where a ∈ (0.5, 1). Finally, we provide a numerical example illustrating the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

For µ ≥ −1/2, and under appropriate conditions on the sequence {Mp}∞p=0 of weights, the elements, the (weakly, weakly*, strongly) bounded subsets, and the (weakly, weakly*, strongly) convergent sequences in the dual of a space Kµ of type Hankel-K{Mp} can be represented by distributional derivatives of functions and measures in terms of iterated adjoints of the differential operator x−1Dx and the Bessel operator Sµ = x−µ−1/2 Dx x 2µ+1Dxx−µ−1/2. In this paper, such representations are compiled, and new ones involving adjoints of suitable iterations of the Zemanian differential operator Nµ = xµ+1/2Dxx−µ−1/2 are proved. Prior to this, new descriptions of the topology of the space Kµ are given in terms of the latter iterations. [ABSTRACT FROM AUTHOR]

In this paper, we study the improved block splitting (IBS) iteration method and its accelerated variant, the accelerated improved block splitting (AIBS) iteration method, for solving linear systems of equations stemming from the discretization of the complex Helmholtz equation. We conduct a comprehensive convergence analysis and derive optimal iteration parameters aimed at minimizing the spectral radius of the iteration matrix. Through numerical experiments, we validate the efficiency of both iteration methods. [ABSTRACT FROM AUTHOR]

Dynamic Pattern Synthesis (DPS) provides a new longitudinal method for evaluating the impacts of macroeconomic and public policy interventions. Situated within complexity theory and critical realism, it has evolved from the established methods of Cluster Analysis and Configurational Modelling approaches. Dynamic Pattern Synthesis identifies case convergence and divergence (using quantitative techniques), while remaining close to the qualitative uniqueness of each case. In this paper, the DPS approach is used to consider macroeconomic convergence across Sub-Saharan Africa during the Millennium Development Goals, and the possible impacts of IMF interventions in stimulating long-term macroeconomic outcomes. The findings reveal a high degree of economic instability experienced across the region and varying responses to an external shock. The importance of 'outliers' and inconsistency in country convergence are also observed. The DPS method highlights the importance of individual country experiences in relation to external shocks. When factoring in IMF interventions, the findings highlight multiple paths to a given policy outcome, rather than a single optimal economic strategy. This opens up the debate on policy issues associated with economic complexity, including how best to create an overall environment of stability that might promote convergence and reduce the instability that undermines planning and investment. [ABSTRACT FROM AUTHOR]

Gender-related issues feature prominently on the EU's agenda and in policies such as the Gender Equality Strategy 2020–2025 which identifies gender equality as a core principle of the EU. Within the broader convergence discourse which examines whether candidate countries are converging with the EU, prompted by Turkey's withdrawal from the Council of Europe Istanbul Convention and the Sofagate incident, this paper conducts a gender-centric convergence analysis in the case Turkey. To this end, it uses five gender-focused indices compiled by the Varieties of Democracy (V-Dem) project. The empirical results from the convergence tests do not provide evidence supporting convergence in terms of these five gender-related indices. The findings of the present study concur with the existing relevant literature and should be viewed in the broader context of Turkey's democratic backsliding and de-Europeanization process. [ABSTRACT FROM AUTHOR]

This paper introduces a class of new extended generalized shift-splitting (NEGSS) preconditioners for solving the 3 × 3 block saddle point problems (SPPs). The algorithm implementation of the NEGSS preconditioner, the convergence of the NEGSS iteration method and the eigenvalue distribution of the corresponding preconditioned matrix with parameter t are investigated. Numerical experiments demonstrate the effectiveness of the proposed method and verify our theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the secure distributed control consensus problem of linear multi‐agent systems (MASs) under switching topologies, subject to intermittent sequential scaling attacks, which was compelled to scaling factor, attack frequency, duration and cooperative‐competitive networks. First, the scenario of a fixed topology is considered, and a novel control protocol combined with a logarithmic quantizer and relative state measurements of neighbouring agents is discussed. The sighed graph is utilized to characterize the communication topology determined by the information flow directions and captured by the graph Laplacian matrix. After that, sufficient conditions for effectiveness of the developed control methods in guiding the MASs to secure bipartite leader‐following consensus are constructed. Second, the scenario of switching topologies is considered, and it is derived that the secure bipartite consensus will be achieved if the designed state feedback control protocol with the scaling factor, the attack duration, attack frequency and switching signal are selected properly. At last, to prove the effectiveness of the designed controllers, a simulation example depended on the real‐word actual military is introduced. [ABSTRACT FROM AUTHOR]

In this paper, a high-accuracy conservative implicit algorithm for computing the space fractional coupled Schrödinger–Boussinesq system is constructed. Meanwhile, the conservative nature, a priori boundedness, and solvability of the numerical solution are presented. Then, the proposed algorithm is proved to be second-order convergence in temporal and fourth-order spatial convergence using the discrete energy method. Finally, some numerical experiments validate the effectiveness of the conservative algorithm and confirm the accuracy of the theoretical results for different choices of the fractional-order α. [ABSTRACT FROM AUTHOR]

The Levenberg–Marquardt (LM) method is one of the most significant methods for solving nonlinear equations as well as symmetric and asymmetric linear equations. To improve the method, this paper proposes a new adaptive LM algorithm by modifying the LM parameter, combining the trust region technique and the non-monotone technique. It is interesting that the new algorithm is constantly optimized by adaptively choosing the LM parameter. To evaluate the effectiveness of the new algorithm, we conduct tests using various examples. To extend the convergence results, we prove the convergence of the new algorithm under the Hölderian local error bound condition rather than the commonly used local error bound condition. Theoretical analysis and numerical results show that the new algorithm is stable and effective. [ABSTRACT FROM AUTHOR]